Quantization Errors of Modulo Sigma-Delta Modulated ARMA Processes

Abstract

In this paper, we study the quantization errors of modulo sigma-delta modulated finite, asymptotically-infinite, infinite causal stable ARMA processes. We prove that the normalized quantization error can be taken as a uniformly distributed white noise for all the cases. Moreover, we find that this nice property is guaranteed by two different mechanisms: the high-enough quantization resolution \cite{Bennett1948}-\cite{WidrowKollar2008} and the asymptotic convergence of quantization errors for some quasi-stationary processes \cite{ChouGray1991}-\cite{LiChenLiZhang2009}, for different cases. But the assumption of the smooth density of the sampled random processes is needed in all the cases.

An abbreviated version of this paper had been published as Li Li, Yudong Chen, "Quantization errors of modulo sigma-delta modulated ARMA processes," Proceedings of IEEE China Summit & International Conference on Signal and Information Processing, pp. 86-90, 2013